#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct bheap {
vector<int> heap, mp;
vector<ll> val;
bheap() {}
bheap(int n) {
val.assign(n, 1e9);
mp.assign(n, -1);
}
void sink(int pos) {
while ((pos << 1) + 1 < heap.size()) {
int l = (pos << 1) + 1, r = (pos << 1) + 2;
int smallest = l;
if (r < heap.size() && val[heap[r]] < val[heap[l]]) smallest = r;
if (val[heap[smallest]] < val[heap[pos]]){
mp[heap[smallest]] = pos;
mp[heap[pos]] = smallest;
swap(heap[pos], heap[smallest]);
} else {
break;
}
pos = smallest;
}
}
bool swim(int pos) {
int p = (pos - 1) >> 1;
if (!(pos && val[heap[p]] > val[heap[pos]])) return 0;
while (pos&&val[heap[p]]>val[heap[pos]]) {
mp[heap[p]] = pos;
mp[heap[pos]] = p;
swap(heap[p], heap[pos]);
pos = p;
p = (pos - 1) >> 1;
}
return 1;
}
void push(int key, ll value) {
int pos = heap.size();
heap.push_back(key);
mp[key] = pos;
val[key] = value;
swim(pos);
}
int pop() {
int n = heap.size(), ret = heap[0];
mp[heap[0]] = n - 1;
mp[heap[n - 1]] = 0;
swap(heap[0], heap[n-1]);
heap.pop_back();
sink(0);
return ret;
}
void update(int key, ll value) {
int pos = mp[key];
val[key] = value;
if (!swim(pos)) {
sink(pos);
}
}
int top() {
return heap[0];
}
bool empty() {
return heap.empty();
}
};
vector<int> intersect[100'005];
vector<pair<int, int>> adj[100'005];
vector<ll> dist[100'005];
vector<int> idx[100'005], mp[100'005];
pair<int, int> rev[2'000'005];
int sparse[17][200'005];
const ll INF = 1e18;
ll min_distance(vector<int> x, vector<int> h, vector<int> l, vector<int> r, vector<int> y, int s, int g) {
int n = x.size(), m = l.size();
for (int i = 0; i < n; i++) {
sparse[0][i] = h[i];
}
for (int j = 1; j < 17; j++) {
for (int i = 0; i < n; i++) {
sparse[j][i] = max(sparse[j - 1][i], sparse[j - 1][i + (1 << (j - 1))]);
}
}
y.push_back(0);
idx[s].push_back(m);
dist[s].push_back(INF);
for (int i = 0; i < m; i++) {
int j = l[i];
while (j <= r[i]) {
if (y[i] <= h[j]) {
intersect[i].push_back(j);
j++;
continue;
}
int mx = 0;
for (int k = 16; k >= 0; k--) {
if (y[i] > max(mx, sparse[k][j])) {
mx = max(mx, sparse[k][j]);
j += (1 << k);
}
}
if (j <= r[i]) {
intersect[i].push_back(j);
j++;
}
}
for (int k = 0; k < intersect[i].size(); k++) {
dist[intersect[i][k]].push_back(INF);
idx[intersect[i][k]].push_back(i);
}
for (int k = 0; k < intersect[i].size(); k++) {
if (k + 1 < intersect[i].size()) {
adj[intersect[i][k]].push_back({intersect[i][k + 1], idx[intersect[i][k + 1]].size() - 1});
}
if (k - 1 >= 0) {
adj[intersect[i][k]].push_back({intersect[i][k - 1], idx[intersect[i][k - 1]].size() - 1});
}
}
}
int cur = 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < idx[i].size(); j++) {
rev[cur] = {i, j};
mp[i].push_back(cur++);
}
}
bheap pq(cur);
pq.push(mp[s][0], 0);
dist[s][0] = 0;
while (!pq.empty()) {
int node = pq.pop();
int i = rev[node].first;
int j = rev[node].second;
ll d = dist[i][j];
j = y[idx[i][j]];
for (auto [nxt, nxth] : adj[i]) {
ll newd = d + abs(x[nxt] - x[i]) + abs(j - y[idx[nxt][nxth]]);
if (dist[nxt][nxth] == INF) {
dist[nxt][nxth] = newd;
pq.push(mp[nxt][nxth], newd);
} else if (newd < dist[nxt][nxth]) {
dist[nxt][nxth] = newd;
pq.update(mp[nxt][nxth], newd);
}
}
}
ll ans = INF;
for (int i = 0; i < dist[g].size(); i++) {
ans = min(ans, dist[g][i] + y[idx[g][i]]);
}
// for (auto i : dist[g]) {
// ans = min(ans, i.first + i.second);
// }
if (ans >= INF) return -1;
return ans;
}
